在時變衰減通道下的結合通道估測與信號偵測演算法和低密度同位元檢查碼之遞迴系統

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(1)國立交通大學電信工程學系碩士論文在時變衰減通道下的結合通道估測與信號偵測演算法和低密度同位元檢查碼之遞迴系統 Joint Channel Estimation, Symbol Detection and LDPC Decoding in Time-Varying Fading Channels 研究生. ：趙必昌. 指導教授：伍紹勳. 中華民國. 九十八. 年. 一月.

(2) 在時變衰減通道下的結合通道估測與信號偵測演算法和低密度同位元檢查碼之遞迴系統 Joint Channel Estimation, Symbol Detection and LDPC Decoding in Time-Varying Fading Channels. 研究生：趙必昌. Student：Pi-Chung Chao. 指導教授：伍紹勳. Advisor：Sau-Hsuan Wu. 國立交通大學電信工程學系碩士論文. A Thesis Submitted to Department of Communication Engineering College of Electrical and Computer Engineering National Chiao Tung University in partial Fulfillment of the Requirements for the Degree of Master in. Communication Engineering January 2009 Hsinchu, Taiwan, Republic of China. 中華民國九十八年一月.

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(5) Joint Channel Estimation, Symbol Detection and LDPC Decoding in Time-Varying Fading Channels. Student:Pi-Chung Chao. Advisor:Dr.Sau-Hsuan Wu. Department of Communication Engineering National Chiao Tung University Abstract An iterative receiver structure for joint channel estimation, symbol detection and channel decoding is proposed for the non-coherent decoding of the low-density parity check code in Rayleigh fading channels. Performance of the proposed algorithm is studied for both the flat and frequency-selective fading channels without using any pilot or training symbol. In flat fading channels, simulation results show that the performance of the non-coherent algorithm is only half decibel inferior to the coherent one, which matches the analysis using extrinsic information transfer chart, while in multiple fading channels, the performance gap against the coherent one is still large, which requires further investigations.. ii.

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(7) ê Z`. i. zZ`. ii. *. iii. ê. iv. %ê. vi. 1 +. 1. 2 Ùÿl. 3. 2.1. Ùÿl: FXÐ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3. 2.2. Ùÿl: #[Ð . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3. 3 Ã y EM Õ ° Ð ) ; ¼ £ ? * r ? Õ ° 3.1. 3`¿c<3;¼ìÃyEMÕ°ÝÐ);¼£?*r? Õ° . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3.2 3.3. 6. 3ÌSI<3;¼ìÃyEMÕ°ÝÐ);¼£?*r?Õ° 11 BCJR -5D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4 Ð ) ; ¼ £ ? * r ? Õ° LDPC D L ] Ù 4.1. 5. LDPC D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv. 16 17 17.

(8) 4.2. 4.1.1. ó;F5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18. 4.1.2. lã;F5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19. 4.1.3. tõÕ°(Min-Sum Algorithm) . . . . . . . . . . . . . . . . .. 20. 4.1.4. LDPC DM»` . . . . . . . . . . . . . . . . . . . . . . . .. 20. );¼£?*r?Õ°LDPCDL]Ù . . . . . . . . .. 21. 5 EXIT Chart 5 . 23. 6 ÿa. 25. 6.1. Ð)JEDBCJRL]PÙÝÿa . . . . . . . . . . . . . . . . . .. 25. 6.2. LDPC_DÝÿa . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 26. 6.3. Ð)JEDBCJRLDPCL]PÙÝÿa . . . . . . . . . . . . .. 29. 6.3.1. `¿c<3;¼ . . . . . . . . . . . . . . . . . . . . . . . . . .. 29. 6.3.2. ÌSI <3;¼ . . . . . . . . . . . . . . . . . . . . . . . . . . .. 36. 7 ¡. 38. ¢Z¤. 39. v.

(9) %ê 2.1. FXÐÙÿl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3. 2.2. #[ÐÙÿl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4. 3.1. JEDÕ°î%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10. 3.2. £GFL2P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13. 3.3. VÙÿl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 14. 3.4. £?;¼8». . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 16. 4.1. Tanner Graph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18. 4.2. ó;F>FLî%. . . . . . . . . . . . . . . . . . . . . . . . . . .. 19. 4.3. lã;F>FLî%. . . . . . . . . . . . . . . . . . . . . . . . . . .. 19. 5.1. )ó;FD ?. 23. 6.1. Compared BER of JED+BCJR case and Ideal Channel case in flat-fading channel. 6.2. v.s.lã;FD. .. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 25. Compared BER of JED+BCJR case and Ideal Channel case in ISI-fading channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 26. 6.3. LDPC in AWGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 27. 6.4. EXIT Chat analysis of LDPC in AWGN in 1.8dB . . . . . . . . . . . . .. 27. 6.5. LDPC in ideal flat-fading channel . . . . . . . . . . . . . . . . . . . . . .. 28. 6.6. EXIT chat analysis of LDPC in ideal fading channel in 4.3dB . . . . . .. 28. 6.7. system model of ”Ideal channel+BCJR+LDPC” . . . . . . . . . . . . . .. 29. vi.

(10) 6.8. Joint BCJR and LDPC system under ideal flat-fading channel in BCJR side with DBPSK modulation . . . . . . . . . . . . . . . . . . . . . . . .. 6.9. 30. Joint BCJR and LDPC system under ideal flat-fading channel in LDPC side with DBPSK modulation . . . . . . . . . . . . . . . . . . . . . . . .. 30. 6.10 EXIT Chart analysis of joint BCJR and LDPC system under ideal flatfading channel with DBPSK modulation in 6.6dB . . . . . . . . . . . . .. 31. 6.11 Joint JED and BCJR and LDPC system under flat-fading channel in BCJR side with DBPSK modulation . . . . . . . . . . . . . . . . . . . .. 32. 6.12 Joint JED and BCJR and LDPC system under flat-fading channel in LDPC side with DBPSK modulation . . . . . . . . . . . . . . . . . . . .. 32. 6.13 EXIT Chart analysis of joint JED and BCJR and LDPC system under flat-fading channel with DBPSK modulation in 7.2dB . . . . . . . . . . .. 33. 6.14 Joint JED and BCJR and LDPC system under flat-fading channel in BCJR side with DQPSK modulation . . . . . . . . . . . . . . . . . . . .. 34. 6.15 Joint JED and BCJR and LDPC system under flat-fading channel in LDPC side with DQPSK modulation . . . . . . . . . . . . . . . . . . . .. 34. 6.16 Simulation of DBPSK + LDPC metric in reference [9] . . . . . . . . . . .. 35. 6.17 compared BER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 35. 6.18 Joint JED and BCJR and LDPC system under ISI channel in BCJR side with DBPSK modulation . . . . . . . . . . . . . . . . . . . . . . . . . . .. 36. 6.19 Joint JED and BCJR and LDPC system under ISI channel in LDPC side with DBPSK modulation . . . . . . . . . . . . . . . . . . . . . . . . . . .. vii. 37.

(11) Chapter 1 + 3Pa;GÙ, FXÝ*rºåÕ`<3;¼(time-varying fading channels) õP{úçÓG(AWGN)ÝÅ(. Q3#[Ð, ;¼£G;ðÎP°ÿáÝ. y Î;¼£?3Pa;GÙµWÝ×Í¥ÝÃ;. rGr(pilot symbols) õ IY*r(training symbols) ÝáÎ×Íð¸àà¼X;¼£?Ý×Í]°. ¬9øÝ]°Qº¸Ùª´*×°(capacity). Ý¹9øÝª´, &ÆÄ6 ¸àß(blind) ;¼£?Õ°¼ãYàÝá×°áGr¼BÃ ;¼£?Ý ]°. Ð);¼£?*r?(joint channel estimation and symbol detection,(JED) Õ°Î×Í|£?`<3;¼õ*r?ÝßÕ°m¢ÝáGr. &ÆÝJEDÕ°Ï×gè"~Î3 [1]. Ãy [2] ÝL]PEM Õ°(recursive expectation-maximization algorithm), JEDÕ°|3^b¢¯áÝ;¼T *r£Gì, EN×Í#[*rD«Ý £?;¼õ?*r. ãy&ÆJED Õ°£?Ý;¼£Gºb8»Ý®Þ,X|&ÆºÞ&ÆÝJEDÕ°¤g5_D(differential code) ¸à|X9Í®Þ. ±Û!-lãD(low-density parity check ,(LDPC)) _DÎ×Ë=b&ðÒ ÷Ý!-lãÎpÝaP sD. 9Ë_D|èº&ð#Shannon \&Ý ý0?Ñæ. LDPC _DÏ×gèÎ3-1960 OãGallager Xè [3]. 3è¡Ý35O. Ý@~QãyþnÝ*zW. . 1. t¥ÝW.

(12) Tanner 31981 OèÝTanner graphs [4]. 3Tanner Ý@~W, ¸ÞLDPC _ D% ;,|% Ý]P¼ÕLDPC _D. àÕ1990 O, LDPC _D39 Ý@~¥±èR [5–7]. 3LDPC D, &Æ;ð¸àõÕ°(sum-product algorithm,(SPA))ÝD° [8]. 3&ÆÝ@~ÿa, ×Ë±ÓÝLDPC D°-t õÕ°(min-sum algorithm) [8] Þ¸à. 3Z¤ [9], [10], ®ïà#)-5_DõLDPC _D3`¿c<3;¼ì. ÿa. 39ËÙì, ;¼£?Þm¸à. hË]°ÿa&ÆÞº3¡ «à¼«&ÆÝÿa®f´.3Z¤ [11], [12], [13], ®ïáÝr*r¼QÃ W)3 s¿c<3;¼(block-flat-fading)ìÝ;¼£?,*r?,õLDPC D ÝÙ.3&ÆÝ@~, &ÆÝJED Õ°Þº)BCJR -5DÕ°õLDPC D® ÙÝ#[Ð. «îZ¤f´, &ÆÝ#[Ù¬|¸à3`¿c< 3;¼ì, ô!ø|¸à3ÌSI(interSymbol-interference)<3;¼ì, 9¸ÿ& ÆÝÿaÙ?!)Ë@(ìÝPa;GÙ. «Z¤ [11], [12], [13] !, &ÆÝ @~mÜ²áÝr(IY)*r, µA!GBÝ, 9ø&Æ|¹ª´ ÄÝ(capacity),¦ÙÝ[Ç. ² I £ G » É ` a(extrinsic information transfer(EXIT) chart) [14] õ Û ;(density evolution,(DE)) [15] Î ðàÝ5 LDPC L]P ÙÝ

(13) Ì. ã9 °5

(14) Ì, &Æ|ï?&ÆÝL]PÙÝ , |¢ã9°ï?5ÙÝ t·;LDPC _D, ;6ÝÆÿaXmÝ`. .3 [16], [17], [18], [19]Z¤ ,®. ï¿àÝEXIT chart 5&Ë!_DÝL]PÙÝ ÿP. 3Z¤ [11],® ï¸àÝÎEXIT chart¼5Ù,3 [12], [13] , ®ï¸àÝÎDE¼5. 3& ÆÝ@~, &ÆÞ¢ [16]Ý]°¸àEXIT chart ¼5&ÆÝ)JEDBCJR õLDPC L]PÙÝ ÿP.. 2.

(15) Chapter 2 Ùÿl 2.1. Ùÿl: FXÐ. s. LDPC. 編碼器. ∏. 離散器. DBPSK. 差分調變器. 衰減通道. ∏:. Figure 2.1: FXÐÙÿl. &ÆÝFXÐÝÿlAFig: 2.1, Xî. H&Æ|:ÕÙÝ-´B ÄLDPC _D. , Q¡_ÄDÝ-3BÄÒ÷. ¡X -5_D. CW*r¡. Xá`<3;¼.. 2.2. Ùÿl: #[Ð. AFig: 4.2Xî,#å. #[ÕBÄ;¼¡Ý*r¡, ´*rÞºBÄ&Æ. ÝJED Õ°£?;¼C?*r. 3BÄBCJR -5DC. Ò÷. Q¡ áLDPC D. . LDPC D 3. ¡, *rÞX. ¼Ý²I(extrinsic)íÞº.

(16) 端. BCJR ξ y. -. -. 解離散器. ∏ −1 :. ∏ −1. c. LDPC. BCJR. JED. 演算法. -. 解碼器. ∏. -. 離散器. ∏:. 解碼器. s. 端. LDPC. Figure 2.2: #[ÐÙÿl. X BCJR D. ®3GÝ(prior)£G. BCJR D. Þº¿à9Í3GÝ(prior)£. GÕ±Ý²I(extrinsic)3GÝ(prior) £GQ¡X/JED Õ°. JED Õ°ÞT¿à9Í±Ý3GÝ(prior) £Gõ;¼[ÕÝÌ?*r±Ý² I(extrinsic)£GBCJR D. . 9øÝD«L]Þº¹ ÕàÕ¾Õ&Æ. ï'ÝL]góºc.. 4.

(17) Chapter 3 Ã yEM Õ ° Ð ) ; ¼ £ ? * r ?Õ° 解離散器. ∏ −1 : ξ y. -. -. c. LDPC. BCJR. JED. 演算法. ∏ −1. -. 解碼器. ∏. -. 解碼器. s. 離散器. ∏:. 39Ía;, &ÆÞº"îA¢3!P²Ý;¼ì¸àEM Õ°¼W& ÆÝJED Õ°,¢ãEM Õ°[eÝP², &Æ|3Õ°L]Æ¡ÿÕ% [eÝ. ´&Æº&ÆÝÕ°'×Í;¼VÿlQ¡¿àEM Õ° ¼.0&ÆÝ;¼£?C*r?ÝÕ°. Õ°£?Ý;¼C?Ý*r £G|!`ÿ. t¡BÄBCJR -5D. ¡, *rÞºDWæÝ. -. ¸àJED ÝÿaÞº«¸àá§;¼Ýÿa3¡«Ýÿaa ;Þº®f´.. 5.

(18) 3.1. 3 ` ¿ c < 3 ; ¼ ì Ã y EM Õ°ÝÐ); ¼£?*r?Õ°. L#[*rym . ym = hm xm + nm. Ím Î`. ¢ó.. Auto-Regressive ;¼VÿlLAì ˜m−1 + BVm hm = F h ¯ Í ˜m−1 = [hm−1 , hm−2 , · · · , hm−Lh ] h ¯ Lxm , hm , ym ¯ ¯ ¯ xm = [x1 , x2 , · · · , xm ], hm = [h1 , h2 , · · · , hm ], ym = [y1 , y2 , · · · , ym ] ¯ ¯ ¯ Q¡ãì2P&Æ|.0£?Ý;¼ X ˆ m−1 = max arg log p(y , hm ) = max arg log p(ym , hm , xm ) h hm hm ¯m ¯ xm ¯ ¯ ¯ ¯ &Æ|EM Õ°ÿÕ2PAì X. l-1. ˆ ) log p(ym , hm , xm )p(xm | ym , h m hm ¯ ¯ ¯ ¯ ¯ ¯ xm ¯ ˆl-1 ] = max Exm [log p(ym , hm , xm ) | ym , h m hm ¯ ¯ ¯ ¯ ¯ ¯. ˆ l = max h m. 6. (3.1).

(19) ˆl-1 ) Aì LQm (hm | h ¯ ¯m ˆl-1 ) , Ex [log p(y , hm , xm ) | y , h ˆl-1 ] Qm (hm | h m m m ¯ ¯ ¯ ¯m ¯ ¯ ¯m ¯ = Exm [log p(ym | hm , xm ) + log p(xm ) ¯ ˜m−1 ) + log p(y ˆl-1 ] + log p(hm | h , hm−1 , xm−1 ) | ym , h m m−1 ¯ ¯ ¯ ¯ ¯ ¯ l-1 l-1 ˆ ] ˆ ) + Exm [log p(xm ) | ym , h = Qm−1 (hm−1 | h m ¯ ¯m−1 ¯ ¯ ¯ ˆl-1 ] + log p(hm | h ˜m−1 ) + Exm [log p(ym | hm , xm )ym , h m ¯ ¯ ¯ ¯. (3.2). ãylog p(xm ) ×ðó, &Æ|ÞÍE¯. X|BÄÕ¡&Æ|ÿÕ ˆl-1 ] Exm [log p(ym | hm , xm )|ym , h m ¯ ¯ ¯ ˜m−1 ) log p(hm | h ¯. ∼ ˆl-1 ] (3.3) = −Exm [1σn2 k ym − hm xm k2 | ym , h m ¯ ¯ ¯ ∼ ˜m−1 ) ˜m−1 )H (BB H )−1 (hm − F h = −(hm − F h ¯ ¯ (3.4). t¡&ÆÞ(3.3) õ(3.4) á(3.2) õ(3.1) , &Æ|ÿÕ ˆl-1 )) ˆ l = max(Q (hm | h h m m hm ¯m ¯ ˆl-1 ) − Ex [1σ 2 k ym − hm xm k2 | y , h ˆl-1 ] = max(Qm−1 (hm−1 | h m−1 n m m m hm ¯ ¯ ¯ ¯ ¯ ˜m−1 )H (BB H )−1 )(hm − F h ˜m−1 )) − (hm − F h ¯ ¯ l-1 1 H H 2 ˜ ˆ = max(Qm−1 (hm−1 | h ˜m + ym x˜H m−1 ) − 2 [ym hm x m hm − k hm k ℵm ] hm ¯ ¯ σ H H −1 ˜m−1 )) ˜ − (hm − F hm−1 ) (BB ) (hm − F h ¯ ¯. (3.5). ˜ m LAì Í˜ xm õ ℵ ˆl-1 ] x˜m = Exm [xm | ym , h m ¯ ¯ ¯ ˆl-1 ] ˜ m = Ex [k xm k2 | y , h ℵ m m ¯m ¯ ¯. 7. (3.6) (3.7).

(20) t;ÝM»&ÆÞ¸àL]PÝt·;Ý]P¼¾Õ ˆl-1 ˆl-1 ) ˆl-1 Fh l ∂ 2 Qm (hm | h m−1 m −1 ∂Qm (hm | hm ) ˆ ¯ ¯ )| ¯ ¯ )| hm = [ ¯l-1 ] − [( ˆ l-1 ] [( ˆ l-1 ] (3.8) ˆ∗ ∂h ˆT ˆT hm =F hm−1 hm =F hm−1 ¯ ˆ ∂ h ∂ h h m m m ¯ ¯ ¯m−1 ˆ l-1 ∂ 2 Qm (hm |hm ) BÄÕ[( ∂ hˆ ∗¯∂ hˆ T¯ ) m. m. |. ˆ l-1 ] hm =F hm−1. ¯. ˆ l-1 ∂Qm (hm |hm ) õ[( ) ˆT ¯ ∂¯h m. |. ˆ l-1 ] hm =F hm−1. , &Æ|ÿÕ. ¯. l-1. ˆ ) ∂Q (h | h 1 1 ∗ ˜ mF h ˆl-1 ] [( m ¯m ¯m ) | [ ][˜ x y − ℵ l-1 ] = m m ˆ ˆT hm =F hm−1 ¯m−1 σn2 0 ∂h m ¯ ¯. (3.9). ˆl-1 ) ˆl-1 ) ∂ 2 Qm−1 (hm−1 | h ∂ 2 Qm (hm | h m ¯ ¯m−1 )] ¯ ¯ ) |hm =F hˆ l-1 ] = [( [( ∗ T m−1 ∗ T ˆ ˆ ˆ ˆ ∂h ∂h ∂h ∂h m. m−1. m. m−1. 1 1 1 ˜ − [ ](BB H )−1 [1 | −F ] − 2 [ ]ℵ m [1 | 0] H ¯ −F σn 0 ¯ (3.10). &Æ#ì¼L(3.10), −Pm−1 , &Æ|ÿÕ −1 −Pm−1 = −Pm|m−1 −. 1 1 ˜ [ ]ℵm [1 | 0] ¯ σn2 0 ¯. (3.11). Í . . .  H. 1  0 0¯   BB + F Pm−1 F H −1 −1 Pm|m−1 = [ ](BB ) [1 | −F ]] = +[  −F H 0 Pm−1 Pm−1 F H ¯. H. F Pm−1   Pm−1 (3.12). 8.

(21) ãDÎp2P 1 1 ˜ [ ]ℵm [1 | 0]−1 ¯ σn2 0 ¯ J 1 −1 −1 −1 −1 = Pm|m−1 − Pm|m−1 [ ][σn2 + [J H | 0]Pm|m−1 [ ]]−1 [J H | 0]Pm|m−1 ¯ ¯ 0 0 ¯ ¯ J −1 −1 −1 −1 = Pm|m−1 − Pm|m−1 − Pm|m−1 [ ][σn2 + J H (BB H + F Pm−1 F H )J]−1 [J H | 0]Pm|m−1 ¯ 0 ¯ (3.13). −1 Pm = −Pm|m−1 −. Þ(3.9) õ(3.13) á(3.8), &Æ|ÿÕ l-1. ˆl h m. ˆ Fh BB H + F Pm−1 F H m−1 ¯ = [ l-1 ] + [ ] Pm−1 F H ˆ h m−1 ¯ × [1 − J[J H (BB H + F Pm−1 F H )J]−1 J H (BB H + F Pm−1 F H )] ×. 1 ∗ ˜ mF h ˆl-1 ] [˜ xm y m −ℵ 2 ¯m−1 σn. (3.14). &ÆÞ&ÆÝJED Õ°ÝM»Àì: EÏmth Í*r,. ˆ `−1 ÝÂ. M»1 : ×Íh m. ˜m M»2 :ãìPÕ˜ xm and ℵ ˆ`−1 ) ∝ p(y | xm , h ˆ`−1 ) p(xm | ym , h m m ¯m ¯ ¯ ¯ (3.15). ˆ ` Q¡/ÕM»2. M»3 : (3.14) Õh m. ˆ m õ˜ ˜ m Ý % £ ? Â. # B Ä ¿ g M »2 õ M »3 Ý ¥ , & Æ | ÿ Õh xm õℵ 9.

(22) ì¼&Æ¹ÕÏ(m + 1)th Í*r.. ˆ m ®Â¼Õ˜ ˜ m+1 . M»4 : ¸à(3.9)?±Pm ÝÂQ¡¸àh xm+1 õℵ. ˆ` M»5 : ã(3.14) Õh m+1 Q¡/ÕM»4.. M»6 : ¥M»1 ÕM»5 àÕt¡×Í*r.. ym. ym −1. hˆ m −2. hˆ m −2. ym +1. hˆ m. hˆ m −1 LLK { xm }. LLK { xm −1 }. hˆ m −1. hˆ m. BCJR. 計算對數似然函數示意方塊 : 估測通道演算法示意方塊 :. Figure 3.1: JEDÕ°î%.. 10. LLK { xm +1 }. hˆ m +1.

(23) 3.2. 3 ` ISI< < 3 ; ¼ ì Ã yEM Õ ° Ý Ð ) ; ¼ £?*r?Õ°. L#[*rym . ym = hm xm + nm. Í hm = [h0 (m), · · · , hL−1 (m)]T x¯m = [xm , · · · , xm−L ]. L:;¼5ó,m:` ¢ó Auto-Regressive ;¼VÿlLAì ˜m−1 + BVm hm = F˘ h ¯ Í ˜m = [hT , · · · , hT h m m−p+1 ] ¯ F˘ = [F1 , F2 , · · · , Fp ]. p:ÿlÝ$ó Lxm , hm , ym ¯ ¯ ¯ xm = [x1 , x2 , · · · , xm ], hm = [h1 , h2 , · · · , hm ], ym = [y1 , y2 , · · · , ym ] ¯ ¯ ¯. 11.

(24) ì¼A!î;Õ¿c<3;¼ìÝµ,&Æ|ÿÕA!(3.2)Ý ˆl-1 ) , Ex [log p(y , hm , xm ) | y , h ˆl-1 ] Qm (hm | h m m m m m ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ˆl-1 ) + Ex [log p(xm ) | y , h ˆl-1 ] = Qm−1 (hm−1 | h m−1 m m m ¯ ¯ ¯ ¯ ¯ ˆl-1 ] + log p(hm | h ˜m−1 ) + Exm [log p(ym |hm , xm )ym , h m ¯ ¯ ¯ ¯. (3.16). #½&ÆLËÍ{úÞg]P:. ˜ m ) , −[h ˜ m − hm ]H C˜ `−1 [h ˜ m − hm ] λ(hm , h m ˜m−1 ] ˜m−1 ]H (BB H )−1 [hm − F˘ h ˜m−1 ) , −[hm − F˘ h η(hm , F˘ h ¯ ¯ ¯. (3.17) (3.18) (3.19). Í ˜ m , (C˜ `−1 )−1 (S˜`−1 )H yi h m m `−1 ˆl-1 C˜m , Exm [xH m xm |ym , hm ] ¯ ¯ ¯ `−1 ˆl-1 ] S˜m , Exm [xm |ym , h m ¯ ¯ ¯. #½Þ(3.16) "vÞ (3.17)õ(3.18)áÿìP. ˜ m ) + η(hm , F˘ h ˜m−1 ) ˆl-1 ) + λ(hm , h ˆl-1 ) w Qm−1 (hm−1 | h Qm (hm | h m ¯ ¯ ¯m−1 ¯ ¯ #ì¼&ÆO ˆl-1 )) ˆ l = max(Q (hm | h h m m hm ¯ ¯m. 12. (3.20).

(25) ˆ m CΞˆm ¸ÍhP h×M»|[ Oì«ÞgPÝh. ˆ m ]H Ξ ˆ m ] ' − [hm−1 − h ˆ m−1 ]H Ξ ˆ m−1 ] ˆ −1 [hm − h ˆ −1 [hm−1 − h −[hm − h m−1 m ˜ m ) + η(hm , F˘ h ˜m−1 ) + λ(hm , h ¯. Function Block 1. 2. x. x. =. z. Vz = Vx (Vx + Vy )H Vy. mz = mx + my. z. Vz = Vx + Vy. m z = Am z. z. x 3. Mean and Variance m z = (Wx + Wy )H (Wx m x + Wy m y ). y. y. +. (3.21). A. 輸入格式: −(x − m ) 輸出格式: −(x − m ) 其中: W = V. Vz = AVx A H. H. Wx (x − m x ). H. Wz (x − m z ). x. z. −1. Figure 3.2: £GFL2P. &ÆÞ¸àFACTOR GRAPHÝÃF¼9×Í]P.SàZ¤ [20] Ý£GFL 2PA Fig: 3.2,&Æ¢ [1] L&ÆÝVÙÿl¢A% Fig: 3.3. Í   Fw , .  F˘L×pL I(LG−1)L×(LG−1)L. 0(LG−p)L×L   0(LG−1)L×L. Jw , [IL×L , 0L×(LG−1)L ]T LG ≥ p ˆ ¯ ˆ m−1 ]H Ξ ˆ −1 µïÿl,´Þ−[hm−1 − h m−1 [hm−1 − hm−1 ]º½hm−1 Ý\aXáFw 3hm Ý ˆ¯ ]H (Ξ ˆ¯ ],ã1ÝÏëÍP|ÿÕ ˆ¯ )−1 [h ¯m − h ¯m − h \aîÿÕ−[h m m m. 13.

(26) λm. Jw. hm −1. F w. hm. +. ◊ hm. =. hm. H J w BB H J w. Figure 3.3: VÙÿl.. ˆ¯ ˆ h m , Fw hm H ˆ¯ ˆ Ξ m = Fw Ξm−1 Fw. ˆ¯ ]H (Ξ ˆ¯ ]Xá”+” ÿÕ−[h¦ −h ˆ¯ )−1 [h ¯ m Ý\aÞ−[h ¯ m −h ¯ m −h ˆ ¦ ]H (Ξ ˆ ¦ )−1 [h¦ − #½º½h m m m m m m m ˆ ¦ ] ,ã1ÏÞPÿ h m. ˆ¯ ˆ¦ = h h m m. (3.22). ˆ¯ ¦ = Ξ ¯ˆ m + Jw BB H JH Ξ m w. (3.23). t¡3” = ”¡Ý\ahm î&Æ|ÿÕ ˆ¯ )−1 h ˆ¯ )−1 [h − (Ξ ˆ¯ )−1 h ˆ ¦ + Jw (S˜`−1 )H ym ]H (Ξ ˆ ¦ + Jw (S˜`−1 )H ym ] [hm − (Ξ m m m m m m m m. 14. (3.24).

(27) Í ˆ¯ , ((Ξ ˆ¯ ¦ )−1 + J C˜ `−1 JH )−1 Ξ m w m m w. (3.25). `−1 ÞC˜m 5WVΛVH ,¸àDÎp2PºÕt¡ÿÕìL]2P:. `−1 H ˆ m = (I − Km )[h ˆ¦ + Ξ ˆ ¦m Jw (S˜m h ) ym ] m. (3.26). ˆm = Ξ ˆ ¦m − Km Ξ ˆ ¦m Ξ. (3.27). `−1 H ˆ ¦ `−1 H ˆ ¦m Jw (I + C˜m Km = Ξ Jw Ξm Jw )−1 C˜m Jw. (3.28). Í. ˆ˜ ˆ ¦ = [(F˘ h ˆ H ]H h )H , h m m−1 ¯m−1. &ÆÞ3ISI;¼ìÝJEDÕ°M»Àì:. ˆ m−1 ÝÂ,¿à#[ÕÝ*rÕ(3.20)õ(3.20). M»1:Â ®h. ˆ ¦ ÝÂ,àC˜ `−1 ñá(3.28)ÕKm . M»2: Îp Ξ m m. ˆ m. ˆ ¦ ñá(3.27)ÿÕΞ M»3: ¸àKm CΞ m. `−1 ˆ m. ,Km á(3.26)ÿÕh M»4: ¸àS˜m. ˆ m ®Â,¿à(3.20)õ(3.20)ÕÏm+1Í*rÝC˜ `−1 CS˜`−1 . M»5: ¸àh m+1 m+1. 15. (3.29).

(28) ˆ m+1 . ˆ m+1 ,¸à(3.26)ÿÕh M»6: ¿à(3.28)C(3.27)?±Km+1 Ξ. M»7: ¥M»5ÕM»6àÕXb*rKÕ±.. 3.3. BCJR - 5 D. 3&ÆÝÕ°,bËÍ2]º¸àÕBCJRD,×ÍÎ3ISI;¼ÝJEDÕ °µìÕ(3.20)õ(3.20),¨×ÍµÎ3JEDÕ°W¡ÞXÕBCJRÕ° ¼-5_D. ´3ISI;¼ÝJEDÕ°µì,ãy#[*r. Kº!88. n,X|&ÆÞ¢Z¤ [21]¸àÉÚÝBCJR¼Õ¸à(3.20)õ(3.20)`Xm ó«QÐó(log-likelihood ,LLK)Â.3JED Õ°¡, &Æ¸àBCJR Õ° ¼D-5_DC. nyBCJR Õ°ÝÞ;|¢Z¤ [22]. &Æ39 ¸à-5_DÝ§ãÎ. &Æ3¸àJED Õ°Ý`Î, £?Ý;¼ºãyEM Õ°Ý¸à®ß8D»Ý®Þ, £?Ý;¼º«Ë@;¼®ß180Ý8É. ¸à-5_D|X9Í®Þ ¸&ÆÝÙJº. Íaÿa3 ÿaa; Fig: 6.1,Fig: 6.2:Õ.. Figure 3.4: £?;¼8».. 16.

(29) Chapter 4 Ð);¼£?*r?Õ° LDPC D L ] Ù 39×a;, &ÆºÞG)JEDBCJRÕ°)LDPC _D¬W L]PÙ|O¾Õ??Ý[¨. 39ÍÙ, &ÆÞº+Û&Õ°. !8D. «FL²Iextrinsic£GÝx, 3¡«Ýa;ÞºbÿaÝ. 3ÍaÏ×ð& ÆÞº+LDPC _D, ÏÞðÞº&ÆÐ)JEDBCJRõLDPCL]P Ùx!8. 4.1. ²Iextrinsic£GFLÝÄ.. LDPC D. 解離散器. ∏ −1 : ξ y. -. -. c. LDPC. BCJR. JED. 演算法. ∏ −1. -. 解碼器. ∏. -. 解碼器. s. 離散器. ∏:. Low-density parity check LDPC _ D Î 31960ãGallager è Ý × Ë Shannon \&Ý×ËaP sD. åÍyþnI**Ýè , E¯Ý35O 17.

(30) ÝLDPC _D90Oãy8²Ý[¥±W #Ý@~Þê. × ÝLDPC _DÎXyA¢'±ÛÝ!-lãÎpH, LDPC ÝDôÎ Ãy9ÍHÝx¼ÆõÕ°SPA. SPA D°Î¢ãÕ\L];FÝ t¯¡^£, 3×góÝL]¡ÿÕt·[. 3#ì¼ÝZa&ÆÞº+ ÛSPAÕ°3ó;Flã;FÝº]PCt¡º+ÛÍZaÿaX¸à± Ó;ÝSP A-tõÕ°min-sum algorithm.. 檢查節點. c0. 變數節點. f0. c1. f1. c2. f2. c3. c4. f3. f4. c5. c6. c7. c8. c9. Figure 4.1: Tanner Graph.. 4.1.1. ó;F5. Ãyt·;Ýt¯¡^£MAP ÝD,&Æm#[ÕÝDCcodeword* rc = [y0 , y1 , · · · yn−1 ] 0FXDCcodewordÝN×Í-ÝÝ¯¡^£APP c = [c0 , c1 , · · · cn−1 ]. ÝÕóÂÝ%,&ÆºÞ9°ÕîWEó«QÐóf £log-likelihood ratio ,LLRÝÕ. 9°APPÝEó«QÐóf£îAì:. L(ci ) , log(. P r(ci = 0|y) ) P r(ci = 1|y). 18. (4.1).

(31) fj rji (b) qij (b). ci y (. 通道觀測信號). Figure 4.2: ó;F>FLî%. ó;FÝ¼:, ãó;Fci FXÕlã;F fj Ý>£G^£L q(ij) = P r(ci = b|inputmessages), b ∈ 0, 1. FX á ci Ý>£GJâÝãXb= #Õci Ýlã;Ffj F¼Ý²Iextrinsic£GC;¼F¼Ý#[*rÝ£G. ãlã; FF¼Ý>£G^£&ÆL rji . &Æ|Þ q(ij) ;¨îWEó«QÐóf£ L(qij ), J|¶WìÝP:. L(qij ) = L(ci ) + Σj 0 ∈Ci \j L(rj 0 i ). 4.1.2. lã;F5. fj. rji (b) qij (b). ci. Figure 4.3: lã;F>FLî%.. 19.

(32) ã l ã ; F ¼ :, X b = # Õf– j˝l ã ; F Ý ó ; Fc– i˝º Þ Í ² Iextrinsic£GXlã;F, BÄ

(33) §¡º3Þ²Iextrinsic£G/Fó;F,h ×

(34) §î rji (b) = P r(checkequationfj issatif iedwithb|inputmessages), b ∈ 0, 1. ¢Z¤ [8], &ÆhàEó«QÐóf£¼î9×Í

(35) §Ä, |¶WAì P. L(rij ) = (Πi0 ∈Vj \i αi0 ) × (φ(Σi0 ∈Vj \i φ(βi0 j )). (4.2). x. +1 Íα = sign|L(qij )| , β = |L(qij )| , Cφ(x) = log( eex −1 ).. 4.1.3. t õ Õ°(Min-Sum Algorithm). tõÕ°ÎjE(4.2)P®«Ý×ËÕ°,ãZ¤ [8]ÿÕìP«P φ(Σi0 φ(βi0 j )) ∼ (βi0 j ))) = φ(φ(min 0 i. =. min βi0 j. i0 ∈Vj \i. 3&Æ?¡Ýÿa,&ÆÞ2àhË«Õ°ãSPAÕ°.. 4.1.4. LDPC DM »`. &ÆÞLDPC

(36) §ÝM»Àì:. 20. (4.3) (4.4).

(37) M»1 : ;. L(qij ) = L(ci ). (4.5). M»2 : ãlã;FFX£G>Õó;F. L(rij ) = (Πi0 ∈Vj \i αi0 ) × (φ(Σi0 ∈Vj \i φ(βi0 j )). (4.6). ∼ = (Πi0 ∈Vj \i αi0 ) × 0min βi0 j. (4.7). i ∈Vj \i. Íα = sign|L(qij )| , β = |L(qij )|. M»3 : ãó;FFX£G>Õlã;F. L(qij ) = L(ci ) + Σj 0 ∈Ci \j L(rj 0 i ). (4.8). M»4 : Õó;FLLRÝõ. L(Qi ) = L(ci ) + Σj 0 ∈Ci L(rji ). 4.2. (4.9). ) ; ¼ £ ? * r ? Õ ° LDPC D L ]Ù. 端. BCJR ξ y. -. -. ∏ −1. c. LDPC. BCJR. JED. 演算法. 解離散器. ∏ −1 :. -. 解碼器. ∏. -. 離散器. ∏:. 21. 解碼器. s. 端. LDPC.

(38) 3Í;&ÆÞ&ÆÝÐ)JEDBCJRÕ°)LDPCDJ®L]PÝº Õ,W×L]PÙÍL]ÕøAì:. M»1: BÄ;¼Ý*rãJEDÕ°#[Õ, ;¼£?C*rLLR?.. M »2: ÞJED£ ? Ý * rLLRX áBCJR Õ ° Ù - ÝLLRX á Ò ÷ ,Q¡XáLDPCD .. M »3: LDPC/ L ]2g ¡ Ýextrinsic£ G X Õ Ò ÷. ,Q ¡ X / BCJR Õ. ° ®£G, BCJR¸àh£GCîgJEDFX¼Ý*rLLR£G/F JEDÝ£G.. M»4: JED¸àBCJR/F*r£GCBÄ;¼Ý*r£G¥±ºÕ °.. M»5: ¥M»1ÕM»4àÕ&Æ'ÝL]gó.. Íaÿaº3ÿaÝa;+Û.. 22.

(39) Chapter 5 EXIT Chart 5 ²I£G»ÉàEXIT chart Î×Ëà¼5ï?D«PD?#[ÙÝ[ e Ý]°. N×ÍàWÝD? . KÎà!>Ý»ð©P¼î. D?. Ý²Iextrinsic£GøðÞºi3EXIT chart î. DÄ9Íà, &Æ|ï. ?&Æ'ÝL]PD?ÙÝ ¨.. LDPC. 結合偵測器及變數節點解碼器偵測器 y. JED. 演算法. -. BCJR. -. 解碼器. 檢查節點 CND. 解離散器. ∏ −1:. I E,DET. ∏. I A ,DET ∏:. −1. ∏. 23. ?. I E,VND. ∏ −1. -. c. 離散器. Figure 5.1: )ó;FD. 解碼器. VND. -. VND. 變數節點. ∏. -. I A ,VND. v.s.lã;FD. ..

(40) 3#ì¼ÝZa, &ÆÞ¢ [16]ÞBi)?. CLDPC _DóF. LDPC lãFÝEXIT chart5%ÝM» M»1 : ¸àMonte Carlo ÿaÕ?. ÝEXIT Ðóvýî¸. IE,DET (IA,DET , SN R). M»2 : )?. (5.1). CLDPC _DóFÝEXIT Ðó.´&Æ|ÌDÕIA,DET. IA,V N D Îb8n=Ý. ¸ÆÝn;P|î ìP p IA,DET = J( dv • J −1 (IA,V N D )). (5.2). Ídv Îîð!Ýó;FùóJ(·) ÐPJÎLZ¤ [16] 8!.X|) ?. CLDPC _DóFÝEXIT Ðóî q IE,V N D = J( (dv − 1)[J −1 (IA,V N D )]2 + [J −1 (IE,DET )]2 ). (5.3). M»3 : LDPC _DÝlãFÝEXIT ÐP|î. IE,CN D = 1 −. D X. p bi • J( dc,i − 1 • J −1 (1 − IA,CN D )). (5.4). i=1. Í dc,i : &Ñ!lãFùóÏith Íùó bi : lãFâbùódc,i Ýf£. M»4 : &Æ¸à(5.1), (5.2), (5.3), (5.4) ¼W&ÆD«PD(?)'ÝEXIT Chart. Extrinsic >!ðÝªôºî3%î. 5Ýÿa&ÆÞº3ì× a:Õ.. 24.

(41) Chapter 6 ÿa 6.1. Ð) JED BCJRL L] P Ù Ý ÿ a 0. 10. ideal fdTs0.01. −1. BER. 10. −2. 10. −3. 10. −4. 10. 5. 10. 15. 20. 25. 30. SNR. Figure 6.1: Compared BER of JED+BCJR case and Ideal Channel case in flat-fading channel. 25.

(42) Compared EMISI v.s. IdealISI fdTs=0.005 107 samples. 0. 10. IdealISI EMISI −1. 10. −2. BER. 10. −3. 10. −4. 10. −5. 10. −6. 10. 5. 10. 15. 20. SNR. Figure 6.2: Compared BER of JED+BCJR case and Ideal Channel case in ISI-fading channel 3î«ËÍ%,&Æ"îÝ¸àDBPSKÝÐ)JED BCJRL]PÙ 3`¿c<3;¼(Fig: 6.1)õÌSI<3;¼(Fig: 6.2) ËË!;¼ìÿa %,¬v3%º'§;¼áÝÿa®f´. ã%&Æ|s¨, 3 `¿c<3;¼ìÝÐ)JEDCBCJR L]PÙûÒá§;¼Ýÿa& ð#, V-û1dB.¬3ÌSI <3;¼ìÝÝ-ûJÿ.. 6.2. LDPC_ _D Ý ÿ a . 39×;Þ"î&ÆX¸àÝLDPC D. Ýÿa[%,5½qA3P. {úçÓG(AWGN)C§`¿c<3;¼Ë;!;¼ì®ÿa, Q¡¸ àEXIT chart 5ËË!;¼ì. qA5, 3P{úçÓG ìEXIT chart 5Ýã@&ðÞã¬3`¿â<3;¼ìJ0-,¬-û. 26.

(43) Î&ð. AWGN+LDPC. −1. 10. −2. BER. 10. −3. 10. −4. 10. −5. 10. 0.4. 0.6. 0.8. 1. 1.2. 1.4 SNR. 1.6. 1.8. 2. 2.2. Figure 6.3: LDPC in AWGN. AWGN EXIT 1.8dB 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0. 0. 0.1. 0.2. 0.3. 0.4. 0.5. 0.6. 0.7. 0.8. 0.9. 1. Figure 6.4: EXIT Chat analysis of LDPC in AWGN in 1.8dB 27.

(44) Ideal Fading +LDPC 100itr. 0. 10. −1. 10. −2. BER. 10. −3. 10. −4. 10. −5. 10. −6. 10. 2. 2.5. 3. 3.5. 4. 4.5. 5. 5.5. SNR. Figure 6.5: LDPC in ideal flat-fading channel. Ideal fading EXIT 4.3dB 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0. 0. 0.1. 0.2. 0.3. 0.4. 0.5. 0.6. 0.7. 0.8. 0.9. 1. Figure 6.6: EXIT chat analysis of LDPC in ideal fading channel in 4.3dB. 28.

(45) 6.3. Ð) JED BCJR LDPCL L] P Ù Ý ÿ a . 3 9 × a ; ,& Æ º 5 ½ q A ; ¼ ÿ l Ý ! 5 W ` ¿ c < 3 ; ¼ C ` ISI<3;¼ËËµ¼"î&ÆÝÐ)JEDBCJRLDPCL]PÙÝÿa .. 6.3.1. `¿c<3;¼. 39×;&ÆÞº"î3`¿c<3;¼ì,&ÆÝÐ)JEDBCJRLDPCL ]PÙÝÿa.´Fig: 6.8 õFig: 6.9, &Æº:Õ3'á§¿c<3 ;¼ì, ¸àDBPSKÐ)BCJRLDPCL]PÙÝÿa. ;ÿlAFig: 6.7Xî. ãÿaáP¡Î3 BCJRÐTÎLDPCÐ, [/º ½L]Ýgó ?,ÕÝ×góÝL]¡, J[J y%?. 3§;¼µ ìÝEXIT chart 56.6dBJ&ÆÝÿa0-Vy1dB(!Ý a !ÝÙL]gó, äaNgÙL]`LDPC/IL]Ýªa).. BCJR. 端. 端. 解離散器. LDPC. ∏ −1 :. y. 已知理想通道. -. ∏ −1. c. LDPC. BCJR. 解碼器. ∏. -. 解碼器. 離散器. ∏:. Figure 6.7: system model of ”Ideal channel+BCJR+LDPC”. 29. s.

(46) DBPSK IDEAL BCJR+LDPC 2(LDPC)X11 iterations (109 samples fdTs=0.01 BCJRside). 0. 10. −1. 10. −2. BER. 10. −3. 10. −4. 10. −5. 10. −6. 10. 5. 5.5. 6. 6.5 SNR. 7. 7.5. 8. Figure 6.8: Joint BCJR and LDPC system under ideal flat-fading channel in BCJR side with DBPSK modulation. 9. DBPSK IDEAL BCJR+LDPC 2(LDPC)X11 iterations (10 samples fdTs=0.01 LDPCside). 0. 10. −1. 10. −2. BER. 10. −3. 10. −4. 10. −5. 10. −6. 10. 5. 5.5. 6. 6.5 SNR. 7. 7.5. 8. Figure 6.9: Joint BCJR and LDPC system under ideal flat-fading channel in LDPC side with DBPSK modulation 30.

(47) EXIT of IDEAL CHANNEL+BCJR+LDPC SNR=6.6dB 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0. 0. 0.1. 0.2. 0.3. 0.4. 0.5. 0.6. 0.7. 0.8. 0.9. 1. Figure 6.10: EXIT Chart analysis of joint BCJR and LDPC system under ideal flatfading channel with DBPSK modulation in 6.6dB. #ì¼&Æ"îÝÎ¸à&ÆÝDBPSKL]PÐ)JEDBCJRLDPCÙ Ýÿa,Ù%AFig:4.2Xî.á§!¼ÿav«,P¡ÎBCJRÐT ÎLDPCÐ, ôÎº ½L]gó?, 3×ÝL]gó¡[ôº y% ÷õ?. ïÝ[fá§;¼Ý´-.. 31.

(48) DBPSK FULL ITERATION JEDLDPC 2(LDPC)x11 iterations ( 109 SAMPLES fdTs=0.01 BCJRside) 0 10. −1. 10. −2. BER. 10. −3. 10. −4. 10. −5. 10. −6. 10. 5. 5.5. 6. 6.5. 7. 7.5. 8. 8.5. SNR. Figure 6.11: Joint JED and BCJR and LDPC system under flat-fading channel in BCJR side with DBPSK modulation DBPSK FULL ITERATION JEDLDPC 2(LDPC)x11 iterations ( 109 SAMPLES fdTs=0.01 LDPCside) 0 10. −1. 10. −2. BER. 10. −3. 10. −4. 10. −5. 10. −6. 10. 5. 5.5. 6. 6.5. 7. 7.5. 8. 8.5. SNR. Figure 6.12: Joint JED and BCJR and LDPC system under flat-fading channel in LDPC side with DBPSK modulation. 32.

(49) 3Fig: 6.13&Æ¸àEXIT chart ¼5&ÆÝL]PÙ. 3%,î«ÝÎ )?. Có;FD. ÝEXIT à, ì«ÝÎlã;FÝEXIT à. . Ý. JÎ²I£GøðÝª%. EXIT chart Ý57.2dBûÒ&ÆÝÿaV b0.5dB0-,ª%î5ÝL]gó@jÿaµÝL]gó8 .. SNR=7.2dB 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0. 0. 0.1. 0.2. 0.3. 0.4. 0.5. 0.6. 0.7. 0.8. 0.9. 1. Figure 6.13: EXIT Chart analysis of joint JED and BCJR and LDPC system under flat-fading channel with DBPSK modulation in 7.2dB. ì«Ëù%Î¸àDQPSKÝÿaµ,&Æ©ãt¡×gL]Ý"î,ã% [´G« -. 33.

(50) DQPSK EM+LDPC BCJRside 109 samples. 0. 10. −1. 10. −2. BER. 10. −3. 10. −4. 10. −5. 10. −6. 10. 7. 7.5. 8. 8.5. 9. 9.5. 10. 10.5. SNR. Figure 6.14: Joint JED and BCJR and LDPC system under flat-fading channel in BCJR side with DQPSK modulation DQPSK EM+LDPC LDPCside 109 samples. 0. 10. −1. 10. −2. BER. 10. −3. 10. −4. 10. −5. 10. −6. 10. 7. 7.5. 8. 8.5. 9. 9.5. 10. 10.5. SNR. Figure 6.15: Joint JED and BCJR and LDPC system under flat-fading channel in LDPC side with DQPSK modulation 34.

(51) ì«9ù%Î¢Z¤ [9] ÝÕ°XÿaÝ, ®ï3Za¸àÕ°;¼ DBPSK METRIC. 0. 10. −1. 10. −2. BER. 10. −3. 10. −4. 10. −5. 10. 6. 6.5. 7. 7.5. 8 SNR. 8.5. 9. 9.5. 10. Figure 6.16: Simulation of DBPSK + LDPC metric in reference [9] £?à# -5_D,Q¡XáLDPCD. . ã%:h®°[&Æ. Ýb×ð-û. Compared BER. 0. 10. Ideal channel+ BCJR+LDPC(DBPSK) JED+BCJR+LDPC(DBPSK) JED+BCJR+LDPC(DQPSK) DBPSK+LDPCin ref[9]. −1. 10. −2. BER. 10. −3. 10. −4. 10. −5. 10. −6. 10. 5. 6. 7. 8 SNR. 9. Figure 6.17: compared BER. 35. 10. 11.

(52) î%Î9×;t¡×ùÿa%,&ÆÞGÝw3×R®f´,|:& ÿa[-û.. 6.3.2. ` ISI <3 ;¼. 39×a;&ÆÞ"î3ISI<3;¼ì, &ÆÝJED + BCJR + LDP CÕ° ùà.ãFig: 6.18 õFig: 6.19|:Õ3¸àDBPSKÝL]PÐ)JEDBCJRLDPC Ù3á§`¿c<3;¼õÌSI<3;¼ìÿaf´.. EMIS IBCJRside fdTs=0.005 107 samples 2x10. 0. 10. EMISIBCJRside IdealISIBCJRside. −1. 10. −2. BER. 10. −3. 10. −4. 10. −5. 10. 3. 4. 5. 6. 7. 8 SNR. 9. 10. 11. 12. 13. Figure 6.18: Joint JED and BCJR and LDPC system under ISI channel in BCJR side with DBPSK modulation. 36.

(53) LDPC side fdTs=0.005 107 samples 2x10. 0. 10. EMISILDPC IdealISILDPC −1. 10. −2. BER. 10. −3. 10. −4. 10. −5. 10. 3. 4. 5. 6. 7. 8 SNR. 9. 10. 11. 12. 13. Figure 6.19: Joint JED and BCJR and LDPC system under ISI channel in LDPC side with DBPSK modulation. 37.

(54) Chapter 7 ¡ 3Í@~, &ÆèÝ×Ëm¢r*rTIY*rÝß;¼£?* r?Õ°. hÕ°Â½Ý¸à3`¿c<3;¼ISI<3;¼. ¸àh Õ°,&ÆÞ;6×Pa;GÙ ÝÑ@Ý£?;¼¸àr*rXðÝÙ [Ç. &Æ#½ÞhÕ°)LDPCD. WL]PÙ|Oè>Ù[|¿. 3á§;¼µìÙ[. DÄEXIT chart 5&Æ|ÝÕ&ÆX' L]PÙ ÿP. Î¼DÄh5?×MÝt·;&ÆÝLDPC_D| ÍÿÕ?·Ý[.. 38.

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